Multiplicity Results for a p1x,p2x-Laplacian Equation via Variational Methods

A. Rezvani and Dengfeng Lã¼

Journal of Mathematics, 2024, vol. 2024, 1-10

Abstract: We prove the existence and multiplicity of nontrivial weak solutions for the following p1x,p2x-Laplacian equation involving variable exponents: −div∇up1x−2∇u−div∇up2x−2∇u+up2x−2u=λhx,u,inΩ,u=0,on∂Ω. Using Ricceri’s variational principle, we show the existence of at least three weak solutions for the problem. We also apply the variational method and genus theory to establish the existence of infinitely many solutions. Then, we prove the closedness of the set of eigenfunctions, such that px≡p.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7622379

DOI: 10.1155/2024/7622379

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